The basic properties of the scalarized BHs are rather similar to those
found in [1]} for a quadratic coupling function
They can
be summarized as follows (see Figure REF ).
First,
these spherically symmetric BHs bifurcate from a special Schwarzschild solution
supporting the scalar cloud
(\(i.e.\)  an infinitesimally small scalar field),
with \(\alpha /M^2 \simeq 0.3635\) .
Second, keeping constant the parameter \(\alpha \)  (or, equally, the event horizon radius \(r_H\) ),
the solutions can be obtained continuously in the parameter space,
forming a line, which starts from the smooth GR Schwarzschild limit (\(\phi \equiv 1\) ), and ends at a limiting solution.
Once the limiting configuration is reached, the solutions cease to exist in
the parameter space.
The existence of the `critical'
configuration can be understood from the condition
(REF ), with the determinant \(\Delta \)  vanishing at that point.
Finally, as with the solutions in Ref. [1]},
for a given ADM mass, the entropy of the solutions
is maximized by the Schwarzschild vacuum BH
(although the relative difference is rather small, of order \(10^{-3}\) ).
